Circles - Area, Circumference, Radius & Diameter Explained! - By The Organic Chemistry Tutor
00:0-1 | in this video , we're going to talk about how | |
00:02 | to calculate the area and the circumference of a circle | |
00:07 | . But first let's talk about the radius and the | |
00:10 | diameter of a circle . My drawing is not perfect | |
00:13 | , but we're gonna make the best of that . | |
00:16 | So here is the center of the circle . It's | |
00:19 | a point right at the middle of the circle . | |
00:23 | Now the distance between the center of the circle and | |
00:25 | any point on a circle that is known as the | |
00:29 | radius of the circle , the diameter is twice the | |
00:37 | value of the radius . Yeah . So let's say | |
00:40 | this is the center of the circle . The diameter | |
00:45 | starts from one end of the circle , it passes | |
00:48 | through the center and connects to the other end of | |
00:50 | the circle . So as you can see visually it's | |
00:56 | twice as long as the radius of the circle . | |
01:00 | So we can say that D is equal to to | |
01:06 | our . Now the next thing need to be familiar | |
01:13 | with is the area and its circumference of a circle | |
01:19 | . The area is basically the area of the shaded | |
01:22 | region . To calculate the area of a circle , | |
01:29 | you could use this formula . It's Pie times are | |
01:32 | squared . Now the circumference is basically the distance around | |
01:40 | the edge of the circle . So this is the | |
01:42 | circumference . And to calculate the circumference it's equal to | |
01:46 | two pi times are Now pie is equal to 3.14 | |
01:56 | , 159 2654 . And there are more other numbers | |
02:02 | , you know that go on after that . But | |
02:06 | typically when solving these problems in school , you'll be | |
02:09 | using approximate value of pi , Which is usually 3.14 | |
02:15 | . So now let's work on some problems . Let's | |
02:19 | start with this one , number one , calculate the | |
02:22 | area and circumference of the circle shown below . Use | |
02:26 | Pi equals 3.14 . So let's start with the area | |
02:32 | . The area is equal to pi r squared The | |
02:40 | radius . We can clearly see that the radius of | |
02:43 | this circle is five ft . It's the distance between | |
02:46 | the center and the point on the circle . So | |
02:51 | we have pie times five ft squared , five squared | |
02:59 | is five times five , which is 25 and feet | |
03:03 | times feet gives you square feet . So the units | |
03:06 | of area is always square units square inches , square | |
03:09 | feet , square yards and so forth . Now the | |
03:15 | exact answer for the area of the circle is 25 | |
03:19 | pi square feet . But we're going to get an | |
03:25 | approximation using this value . So let's replace pie With | |
03:34 | 3.14 . So the answer for this problem , the | |
03:46 | area is approximately 78.5 square feet . So that's how | |
03:55 | you can calculate the area of a circle . If | |
03:59 | you're given the radius of that circle , now let's | |
04:03 | move on to the second part of the problem , | |
04:06 | let's calculate the circumference of the circle . So we're | |
04:11 | gonna use the formula C . Is equal to two | |
04:13 | pi R Let's get the exact valley 1st . So | |
04:22 | let's replace the radius with five ft . two pi | |
04:27 | times five is 10 pie . So the exact answer | |
04:30 | is 10 pie feet . So notice that the unit | |
04:34 | for circumference is in feet , which is the same | |
04:37 | as unit for radius , but the unified area is | |
04:40 | in square feet . Now let's replace pie with 3.14 | |
04:47 | . So this will give us an approximate answer 10 | |
04:54 | times 3.14 , It's going to be 31.4 . So | |
04:59 | the circumference of this particular circle is 31.4 feet . | |
05:06 | So if you were to start here , let's say | |
05:08 | on a track and you would let's see where to | |
05:11 | walk around in this circle , You would travel a | |
05:15 | distance of 31.4 ft . So that's what that means | |
05:20 | , Given that The radius of the circle is five | |
05:23 | ft . Now let's work on a similar problem at | |
05:30 | this time . Were given the diameter of the circle | |
05:34 | , the diameter is 14 inches . How can we | |
05:39 | use the diameter to calculate the area and the circumference | |
05:42 | of the circle ? Well , the first thing we | |
05:45 | need to do is we need to find the radius | |
05:47 | . Remember the diameter is twice the length of the | |
05:51 | radius . So if we divide both sides of this | |
05:54 | equation by two we'll get that . The radius is | |
05:58 | half of the diameter , Half of 14 or 14 | |
06:04 | divided by two is 7 . So the radius of | |
06:06 | this circle is 7" . So now that we know | |
06:11 | the radius of the circle , we can calculate the | |
06:13 | area and the circumference . So let's start with the | |
06:16 | area , we know the area is pi R squared | |
06:23 | . So let's replace our with seven inches seven squared | |
06:31 | or seven times 7 is 49 . So we get | |
06:34 | that the area is 49 pi square inches . So | |
06:40 | this right here is the exact answer . But now | |
06:45 | let's replace pie with 3.14 49 times 3.14 . That's | |
07:00 | 1 53.86 . But what we're gonna do is we're | |
07:05 | going around our answer to 154 square inches . So | |
07:15 | that's the area of the circle in this problem . | |
07:21 | Now let's calculate the circumference . The circumference is two | |
07:28 | pi r . Let's replace our with 7" . So | |
07:37 | we have two pi times seven . So we get | |
07:41 | an exact answer of 14 pie inches . Now let's | |
07:47 | get our approximate answer by replacing pie With 3.14 14 | |
08:02 | times 3.14 , That's 43.96 . But since we use | |
08:08 | 3.14 for pie , I'd like to run my answer | |
08:11 | to three significant figures . So I'm going around it | |
08:15 | to 44.0 inches . So that's the approximate value for | |
08:26 | the circumference of the circle . Number two . The | |
08:30 | area of a circle is 28.5 sq in . What | |
08:35 | is the radius of the circle ? So we're gonna | |
08:38 | use 3.14 for pi . We're gonna run our answer | |
08:41 | to the nearest 10th place . So let's start with | |
08:47 | this form of area is equal to pi R squared | |
08:53 | . So we're gonna replace the area with 28.5 sq | |
08:57 | in . And we're going to replace pie with 3.14 | |
09:01 | . We're gonna solve for R . In order to | |
09:05 | do that , we need to divide both sides , | |
09:07 | Bye 3.14 . So we get 28.5 divided by 3.14 | |
09:19 | . And that works out to be 9.07 64 3 | |
09:26 | 3 with some of the numbers . But this should | |
09:28 | be good enough so that is equal to r squared | |
09:31 | to get our we need to take the square root | |
09:33 | of both sides , So the square root of 9.076433 | |
09:44 | . We could around the answer . So let's use | |
09:49 | are approximate symbol . So we're gonna round it to | |
09:52 | 3.01 . So that's the nearest 100th . So this | |
09:58 | is the radius of the circle . That's how we | |
09:59 | could find it . If we're given the area of | |
10:02 | the circle . And by the way , let's not | |
10:04 | forget the unit for radius . The unified area is | |
10:09 | square inches . So the unit for the radius of | |
10:12 | this circle is going to be just inches . The | |
10:15 | radius diameter circumference . They have units like inches , | |
10:20 | feet , yards , Things like that area is always | |
10:23 | square units , so just keep that in mind . | |
10:25 | But these two , they must match number three . | |
10:32 | The circumference of a circle is 14.5 ft . What | |
10:36 | is the diameter of the circle ? So the formula | |
10:42 | that we need to use is circumference is equal to | |
10:45 | two pi r . Now what we need to do | |
10:48 | here is we need to use the circumference to calculate | |
10:51 | the radius of the circle . Once we have the | |
10:54 | radius of the circle , we could then find the | |
10:56 | diameter of the circle because we know that the diameters | |
10:59 | twice the value of the radius of the circle . | |
11:01 | So let's calculate our furs . Let's replace C with | |
11:05 | 14.5 ft . Unless you place pie With 3.14 Two | |
11:16 | times 3.14 , that's 6.28 . So they get our | |
11:22 | by itself , we need to divide both sides by | |
11:26 | 6.28 , 14.5 , divided by 6.28 . We get | |
11:37 | 2.3089 . We're going around it to the nearest 10th | |
11:41 | , I mean to the nearest 100 . So that's | |
11:43 | going to be two 31 Now let's put the units | |
11:50 | . So the universe circumference is in feet . That's | |
11:53 | gonna be the same for the unit of radius . | |
11:57 | So now that we have the radius , we could | |
11:59 | find the diameter , the diameter is simply to our | |
12:03 | it's twice the value of art , So it's going | |
12:08 | to be two times 2.31 , two times 2 is | |
12:14 | four , two times 31 is 62 . So the | |
12:20 | diameter of this circle is gonna be approximately 4.62 ft | |
12:25 | . Number four . The circumference of a circle is | |
12:28 | 18 pie m . What is the area of the | |
12:31 | circle ? Go ahead and try that problem . So | |
12:40 | let's begin with this equation , C . Is equal | |
12:42 | to two pi R . So that's our circumference equation | |
12:47 | . And we also know that the area is pi | |
12:50 | R squared . So those are the two equations that | |
12:53 | we have . So we're given the circumference and we | |
12:57 | need to find in the area . What we need | |
13:00 | to do is we need to use the circumference to | |
13:01 | get the radius once we have the radius , we | |
13:04 | could plug it into the second equation to get the | |
13:06 | area . So let's go ahead and do that . | |
13:10 | So we're gonna replace the circumference with what it equals | |
13:14 | 18 pie meters . Now we're going to solve for | |
13:21 | r To get our by itself , we need to | |
13:23 | divide both sides by two pi on the right side | |
13:29 | to Pie will cancel . On the left side . | |
13:32 | Pie will cancel . And we're going to have 18 | |
13:34 | divided by two , which is nine . So this | |
13:38 | is the radius of the circle , it's nine . | |
13:42 | And since the unit for circumference is in meters , | |
13:45 | the radius is going to be in meters as well | |
13:48 | . So this is an exact answer . So now | |
13:52 | let's use that to calculate the area . So let's | |
13:56 | replace our with nine m nine Squared is 81 . | |
14:01 | So the exact answer for the area will be 81 | |
14:04 | pie square meters . Now , let's get our approximate | |
14:09 | answer . Let's replace pie With 3.14 . So 81 | |
14:22 | times 3.14 . That's 254.34 . So we're going to | |
14:29 | round that to the nearest whole number , Which will | |
14:32 | be 254 . So that's the approximate area of the | |
14:37 | circle . It's 200 54 square meters . That's the | |
14:43 | answer number five . The area of a circle is | |
14:48 | 100 square yards . What is the circumference of the | |
14:51 | circle ? So let's write the two equations that we're | |
14:57 | going to use A is equal to pi R , | |
15:00 | squared and C is equal to two pi R . | |
15:05 | So this problem is basically the reverse of the previous | |
15:08 | problem . Were given the area . We're going to | |
15:10 | use that to calculate our once we have our we're | |
15:13 | going to plug it into this equation to get the | |
15:15 | circumference . So let's replace A with 100 square yards | |
15:24 | And let's plug in Pi as 3.14 . So to | |
15:30 | get our by itself , what we're gonna do is | |
15:31 | we're gonna divide both sides By 3.14 100 , divided | |
15:40 | by 3.14 . That is 31 eight 47 133 And | |
15:49 | that square yards . So to get our we need | |
15:54 | to take the square root of both sides . So | |
16:01 | the square root of 31.847133 , that's 5.6433 three . | |
16:15 | And the square root of yards square . It is | |
16:18 | just yards . So this is the approximate valley for | |
16:23 | the radius . So now we're gonna take that answer | |
16:26 | and plug it in to the circumference equation . So | |
16:30 | we have C is equal to two pi but we're | |
16:32 | gonna use 3.14 for pi and then we're gonna replace | |
16:36 | our with 5.6433 , 3 yards . So you should | |
16:55 | get 35.440 . But we're going to round it to | |
16:59 | the nearest 10th . So we're going to say that | |
17:01 | the circumference is approximately 35.4 and the unit is going | |
17:08 | to be yards . So that's how you can calculate | |
17:11 | the circumference if you know the area of the circle | |
17:14 | . And that's basically it for this video . Thanks | |
17:17 | for watching |
DESCRIPTION:
This basic geometry video tutorial explains how to calculate the area and circumference of a circle given it's radius and diameter. This video contains a few examples with word problems. This video also explains how to calculate the circumference given the area, and how to calculate
OVERVIEW:
Circles - Area, Circumference, Radius & Diameter Explained! is a free educational video by The Organic Chemistry Tutor.
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